All I’m saying is that it depends. Depending on the region, the real-world meaning of a named “city”, “town”, etc. can be a purely administrative construct, a purely demographic construct, or some combination of the two. An administrative city can be a boundary alone, and a demographic city can be a place=* point alone, but when the two concepts have merged in reality, then it gets murkier and depends on local expectations.
For example, about half of the territory of New Orleans is sparsely inhabited swampland (not counting the water area). No administrative boundary corresponds to the settlement, either in OSM or in real life. The overall boundary exists because of the settlement. For all intents and purposes, the place node centered closer to the central business district represents both the core settlement and any outlying areas, both officially and for all anyone cares. No one distinguishes between the two in practice. Even if we were to map centroid points comprehensively, we would not map one for New Orleans, because the existing place node is a more meaningful label.
However, the important context here is that New Orleans is a type of administrative entity that generally does not completely subdivide its parent boundary. Normally, any substantial settlement in Louisiana, such as nearby Slidell, has its own administrative entity that has a boundary shaped vaguely like the settlement. The fact that New Orleans extends into the wilderness is a peculiar exception that recently led the local community on a hundred-message-long journey through 19th-century laws and present-day traffic signs. Thus the distinction between New Orleans as a settlement and New Orleans as an administrative territorial entity is more obscure than it would be in another state where local boundaries normally do not conform to settlements.[1] Another consequence is that place=municipality is completely unused in Louisiana, because nothing officially exists that would require it.
In other words, it isn’t enough that the settlement and administrative entity share the same name: in order for the label role to be appropriate, the two would at least need to be considered two representations of the same thing administratively. Even so, if Wikidata happens to split the two into separate items for its own reasons, then this would theoretically force the boundary relation and its label member to have different wikidata=* tags.
Wikidata does distinguish a New Orleans urban area (Q125805783), but this is merely a statistical reporting unit that intentionally ignores all boundaries and is therefore irrelevant to mapping administrative boundaries. ↩︎